{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# SageMath数学巡游\n",
    "\n",
    "# A Tour of SageMath\n",
    "Cody Luo 罗江林  cody(at)ustc.edu    2019 autumn\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 1 迷上SageMath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3+5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2601983048666099770481310081841021384653815561816676201329778087600902014918340074503059860433081046210605403488570251947845891562080866227034976651419330190731032377347305086443295837415395887618239855136922452802923419286887119716740625346109565072933087221327790207134604146257063901166556207972729700461767055550785130256674608872183239507219512717434046725178680177638925792182271"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2**1277-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_prime(_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "385620482362580421735677065923463640617493109590223590278828403276373402575165543560686168588507361534030051833058916347592172932262498857766114955245039357760034644709279247692495585280000000000000000000000000000000"
      ]
     },
     "execution_count": 44,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorial(128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4294967297\n",
      "641 * 6700417\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'If Euler is living in 21st, will he use \"641divF5\" as his password?'"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fermat5=2^2^5+1;print(Fermat5)\n",
    "fac=factor(Fermat5);print(fac)\n",
    "'If Euler is living in 21st, will he use \"641divF5\" as his password?'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p=17\n",
    "x=2^(p-1)-1\n",
    "x%p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3855, 0)\n",
      "(4, 3)\n",
      "(1, 7, -6)\n"
     ]
    }
   ],
   "source": [
    "print(divmod(x,p))\n",
    "print(divmod(23,5))\n",
    "print(xgcd(13,15))\n",
    "#extended gcd g = sa + tb = gcd(a, b): g,s,t=xgcd(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(2^6 % 13)\n",
    "power_mod(2,6,13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(pi, e, golden_ratio, euler_gamma, I, +Infinity)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.14159265358979324"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc=(pi,e,golden_ratio,euler_gamma,I,oo)\n",
    "print(cc)\n",
    "pi.n(digits=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068"
      ]
     },
     "execution_count": 33,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    " N(pi, digits=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[  -2    1]\n",
       "[ 3/2 -1/2]"
      ]
     },
     "execution_count": 24,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    " matrix([[1,2], [3,4]])^(-1)  # the inverse of a 2×2 matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "arcsinh(x)"
      ]
     },
     "execution_count": 25,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=var('x')\n",
    "integrate(1/sqrt(1+x^2),x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "e"
      ]
     },
     "execution_count": 54,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit((1+x)^(1/x),x=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[x == -1/2*(b + sqrt(b^2 - 4*a*c))/a, x == -1/2*(b - sqrt(b^2 - 4*a*c))/a]"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,a,b,c=var('x a b c')\n",
    "s=solve(a*x^2+b*x+c==0,x);s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1/2*(b + sqrt(b^2 - 4*a*c))/a"
      ]
     },
     "execution_count": 29,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s[0].rhs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 32,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    " show(plot(sin(x) + sin(1.5*x), 0, 6*pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x + y) * (x^2 - x*y + y^2) * (x^6 - x^3*y^3 + y^6) * (x^10 - x^9*y + x^8*y^2 - x^7*y^3 + x^6*y^4 - x^5*y^5 + x^4*y^6 - x^3*y^7 + x^2*y^8 - x*y^9 + y^10) * (x^20 + x^19*y - x^17*y^3 - x^16*y^4 + x^14*y^6 + x^13*y^7 - x^11*y^9 - x^10*y^10 - x^9*y^11 + x^7*y^13 + x^6*y^14 - x^4*y^16 - x^3*y^17 + x*y^19 + y^20) * (x^60 + x^57*y^3 - x^51*y^9 - x^48*y^12 + x^42*y^18 + x^39*y^21 - x^33*y^27 - x^30*y^30 - x^27*y^33 + x^21*y^39 + x^18*y^42 - x^12*y^48 - x^9*y^51 + x^3*y^57 + y^60)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "x^99 + y^99"
      ]
     },
     "execution_count": 36,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R.<x,y>=QQ[]\n",
    "fac=factor(x^99+y^99);print(fac)\n",
    "fac.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10], [9, 1], [8, 2], [8, 1, 1], [7, 3], [7, 2, 1], [7, 1, 1, 1], [6, 4], [6, 3, 1], [6, 2, 2], [6, 2, 1, 1], [6, 1, 1, 1, 1], [5, 5], [5, 4, 1], [5, 3, 2], [5, 3, 1, 1], [5, 2, 2, 1], [5, 2, 1, 1, 1], [5, 1, 1, 1, 1, 1], [4, 4, 2], [4, 4, 1, 1], [4, 3, 3], [4, 3, 2, 1], [4, 3, 1, 1, 1], [4, 2, 2, 2], [4, 2, 2, 1, 1], [4, 2, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1], [3, 3, 3, 1], [3, 3, 2, 2], [3, 3, 2, 1, 1], [3, 3, 1, 1, 1, 1], [3, 2, 2, 2, 1], [3, 2, 2, 1, 1, 1], [3, 2, 1, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [2, 2, 2, 2, 1, 1], [2, 2, 2, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 41,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parts=Partitions(10);print(parts.list())\n",
    "count=parts.cardinality();count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 47,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = random_matrix(RDF,300)\n",
    "eig = m.eigenvalues()  #about 2 seconds\n",
    "w = [(i, abs(eig[i])) for i in range(len(eig))]\n",
    "show(points(w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/6*pi^2\n",
      "1.64490354973576\n",
      "1.64493406684823\n"
     ]
    }
   ],
   "source": [
    "k, n = var('k,n')\n",
    "s=sum(1/k^2, k, 1, oo);print(s)\n",
    "s2=sum(1/k^2, k, 1, 2^15);print(N(s2))\n",
    "print(N(pi^2/6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 48,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x,y: cos(x*y)\n",
    "contour_plot(f, (-4, 4), (-4, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 44 graphics primitives"
      ]
     },
     "execution_count": 49,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = graphs.WheelGraph(15)\n",
    "g.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, -1, 20, 23/5, 4, 3, 81)"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1+1,2-3,5*4,23/5,23//5,23%5,3**4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 4, 1/5)"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(12|8,7&4,~5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'word' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-0a87601706c2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mword\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Upgrade this project. It is on an unpaid trial server. Expect poor performance and no email notifications. — more info...\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'word' is not defined"
     ]
    }
   ],
   "source": [
    "Words(\"Upgrade this project. It is on an unpaid trial server. Expect poor performance and no email notifications. — more info...\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 2 数论实验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3449751"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prime_pi(57989356)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "图论研究 2D作图与3D作图动态交互"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "337"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "previous_prime(344)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
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